Shear, writhe and filaments: turbulence in the high latitude molecular cloud MBM 40

Context. It is almost banal to say that the interstellar medium (ISM) is structurally and thermodynamically complex. But the variety of the governing processes, including stellar feedback, renders the investigation challenging. High latitude molecular clouds (HLMCs) with no evidence of internal star formation, such as MBM 40, are excellent sites for studying the chemistry and dynamic evolution of the cold neutral ISM. Aims. We used this high latitude cloud as an exemplar for the dynamical and chemical processes in the diffuse interstellar medium. Methods. We analyzed new and archival $^{12}$CO, $^{13}$CO, CH, HCO$^+$, CS, H$_2$CO, HCN data from Five College Radio Observatory (FCRAO), Onsala Space Observatory (OSO), Arizona Radio Observatory (ARO) and W. Gordon telescope (Arecibo) combined with the Galactic Arecibo L-band Feed Array HI (GALFA-HI) HI 21 cm data set, to study the chemistry, thermal state, and dynamics of MBM 40. A new dynamical analytical approach was adopted by considering each line profile as a line of sight Probability Distribution Function (PDF) of the turbulence weighted by gas emissivity. Results. The atomic and molecular gas are smoothly distributed in space and velocity. No steep transition is seen between circumcloud atomic and cloud molecular gas in either radial velocity or structure. We proposed a topology of the cloud from the molecular tracers, a contorted filamentary structure that is shaped by a broad embedding shear flow in the neutral atomic gas. Comparative examination of different molecular tracers shows that $^{13}$CO, H$_2$CO and CS arise from only denser molecular cores, where $^{12}$CO, CH and HCO$^+$ traces diffuse gas with broader range of dynamics.